Comunicazione elettriche - i campi elettromagnetici

Equazioni di campo elettromagnetico

[ ]E ( r , t ) V m[ ]H ( r , t ) A m[ ] =Cb A secD ( r , t ) 2Cb m[ ] =B ( r , t ) Wb V sec2Wb m

∆ ρQ (t ) Cb ≡Q (t ) ( r , t ) dvρ =( r , t ) lim∆ ∆V 0 3V m V

[ ]A = ⋅ ⋅ˆ( ) ( , )I t J r t n ds AJ ( r , t ) 2m S

Φ = ⋅ ⋅ˆA n dsS∂

{ }∇ × + =E ( r , t ) B ( r , t ) 0∂t∂

! "{ }∇ × − =H ( r , t ) D ( r , t ) J ( r , t )∂t

ρ∂ ( r , t )∇ ⋅ = −J ( r , t ) ∂td⋅ = − ⋅ ⋅ˆE dl B n dsdtC Sd

! "⋅ − ⋅ ⋅ =ˆH dl D n ds I (t )dtC S

d ρ⋅ ⋅ = −ˆJ ( r , t ) n ds ( r , t ) dvdtS V

# $ ⋅ ⋅ = ∇ ⋅ˆA n ds AdvS V

( )∇ ⋅ ∇ × =A 0% !# % & ⋅ = ∇ × ⋅ ⋅ˆA dl A n dsC S

# δ − =f ( x ) ( x x ) dx f ( x )0 0x ∆ →# S 0

⋅ ⋅ =ˆA n ds 0 A discontinu o∆S 1'

ρ∇ ⋅ = ∇ ⋅ =D ( r , t ) ( r , t ) B ( r , t ) 0

⋅ ⋅ = ⋅ ⋅ =ˆ ˆD ( r , t ) n ds Q (t ) B ( r , t ) n ds 0S S

( $ε µ= = = + = +D E B H D D P B B M0 0[ ] F

{ }+∞ +∞ == ⋅D ( r , t ) dt ' dr ' ( r , r ' ; t , t ' ) E ( r ' , t ' ) 4m secee− ∞ − ∞ % $)

{ }+∞= ⋅D ( r , t ) dr ' ( r , r ' ; t ) E ( r ' , t )# $ e− ∞

* { }+∞) = ⋅D ( r , t ) dt ' ( r ; t , t ' ) E ( r , t ' )% $ e( − ∞

# + # ,%τ τ= −(t , ) (t )% # e e0

ρ ρ= −( r , ) ( r )% e e-+ ..

ε= ⋅D ( r , t ) ( r , t ) E ( r , t )0 /+1 + 2 + 3

ε=# ( r , t ) ( r , t )e( •0

ε ε ε ε• = = = ( r , t )xx yy zz

! ε=D ( r , t ) E ( r , t ) 1 ,0 3

σ = ↔ =0 J 0$ c −r r '